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arXiv:1407.3288 · Physical Review B

Current dependence of the red boundary of superconducting single-photon detectors in the modified hot-spot model

Denis Yu. Vodolazov

Published Aug 22, 2014• 32 citations
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Abstract

We find the relation between the energy of the absorbed photon and the threshold current at which the resistive state appears in the current-carrying superconducting film with probability about unity. In our calculations we use the modified hot-spot model, which assumes a different strength of suppression of the superconducting order parameter in the finite area of the film around the place where the photon is absorbed. To find the threshold current we solve the Ginzburg-Landau equation for the superconducting order parameter, which automatically includes the current continuity equation and it allows us to consider the back effect of current redistribution near the hot spot on the stability of the superconducting state. We find quantitative agreement with recent experiments, where we use the single fitting parameter which describes what part of the energy of the photon goes for the local destruction of the superconductivity in the film.

DOI
10.1103/physrevb.90.054515

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We find the relation between the energy of the absorbed photon and the threshold current at which the resistive state appears in the current-carrying superconducting film with probability about unity. In our calculations we use the modified hot-spot model, which assumes a different strength of suppression of the superconducting order parameter in the finite area of the film around the place where the photon is absorbed. To find the threshold current we solve the Ginzburg-Landau equation for the superconducting order parameter, which automatically includes the current continuity equation and it allows us to consider the back effect of current redistribution near the hot spot on the stability of the superconducting state. We find quantitative agreement with recent experiments, where we use the single fitting parameter which describes what part of the energy of the photon goes for the local destruction of the superconductivity in the film.
We theoretically study the dependence of the intrinsic detection efficiency (IDE) of a superconducting nanowire single photon detector on the applied current, I , and magnetic field, H . We find that the current, at which the resistive state appears in the superconducting film, depends on the position of the hot spot (a region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. This circumstance leads to inevitable smooth dependence IDE(I) when IDE , even for a homogenous straight superconducting film and in the absence of fluctuations. For IDE , a much sharper current dependence comes from the fluctuation-assisted vortex entry to the hot spot, which is located near the edge of the film. We find that a weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation-assisted vortex entry to the hot spot (IDE ), and it weakly affects IDE when the photon detection is connected with the current-induced vortex nucleation in the film with the hot spot (IDE ).
We have experimentally studied the supercurrent-assisted formation of the resistive state in nano-structured disordered superconducting Nb(N) films after absorption of a single optical to near-infrared photon. The efficiency of the resistive state formation has a pronounced spectral cut-off; corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the refined hot-spot model suggests that the quantum yield for near-infrared photons increases with the photon energy. Relaxation of the resistive state depends on the photon energy making the phenomena feasible for the development of energy resolving single-photon detectors.
Dependence of quantum efficiency on energy of a photon for superconducting single-photon detector (SSPD) is modeled. The “hot-spot” model, describing quasiparticle multiplication, their diffusion, local suppression of superconductivity and supercurrent redistribution in the strip of the detector, is utilized. To describe response at low energy of quanta, a concept of fluctuation-assisted nucleation of the resistive state is applied. Qualitative formulas are derived, describing spectral and current dependency of quantum efficiency in the limits of low and high efficiency. The formulas can be used to describe response of SSPD in the whole range of wavelengths. The result allows to specialize conditions of operation corresponding to high values of the detector quantum efficiency. Thereby, absence of red-cutoff for SSPD is theoretically explained, an ability to obtain high quantum efficiency in IR-range is confirmed.
We report an experimental investigation of the hot-spot evolution in superconducting single-photon detectors made of disordered superconducting materials with different diffusivity and energy downconversion time values, i.e., 33-nm-thick NbN and 23-nm-thick NbC films. We have demonstrated that, in NbC film, only 405-nm photons produce sufficiently large hot spot to trigger a single-photon response. The dependence of detection efficiency on bias current for 405-nm photons in NbC is similar to that for 3400-nm photons in NbN. In NbC, large diffusivity and downconversion time result in 1-D critical current suppression profile compared with the usual 2-D profile in NbN.
To elucidate the photon detection mechanism of superconducting single-photon detectors, we theoretically examine the dynamics of type-II superconductors with a bias current using the two-dimensional time-dependent Ginzburg–Landau and the Maxwell equations. The photon injection that weakens the superconducting order parameter is treated phenomenologically as a local temperature increase, and the injected energy is controlled by the initial hotspot radius. The photon is detected by the voltage change between two electrodes attached to the left and right edges of the superconductor. We find that the detection dynamics in certain parameter ranges can be explained by the conventional hotspot model, whereas those in other parameter ranges are governed by the formation and subsequent dynamics of superconducting vortex and antivortex pairs. The photon detection is possible for an initial hotspot radius that exceeds a threshold value. We find that the generation of a vortex–antivortex pair occurs near the threshold. The flow of the pair perpendicular to the current direction finally creates a normal region for the photon detection. The voltage change for the Ginzburg–Landau parameter close to the transition point from type-II to type-I superconductor shows anomalous behavior that is not associated with the dynamics of the vortex–antivortex pair. We also examine the effects of spatially non-uniform current density on the voltage change and the superconducting order parameter to provide a hint to understand the behavior of wide-strip single-photon detectors. The estimated values of incident photon energy and response time for photon detection are reasonable in comparison with experiments. The present analysis provides useful guidelines for flexible design of device structures.
Abstract We show that avoiding bends in a current-carrying superconducting nanowire enhances the probability for low energy photons to be detected and that this enhancement is entirely due to the increase in the experimentally achievable critical current. We studied nanowires shaped as either meander or spiral. The spirals had different layouts, a double-spiral layout with an S-turn in the middle and a single-spiral layout without such a turn. Nanowires were prepared from films of niobium nitride with a thickness of 5 nm. For specimens with each layout we measured the spectra of the single-photon response in the wavelength range from 400 nm to 1600 nm and defined the cut-off wavelength ( λ c ) beyond which the response rolls off. The largest and the smallest λ c were found for the single-spiral layout and for the meander, respectively. For all three layouts the relationship between λ c and the relative bias current falls onto a universal curve which has been predicted earlier in the framework of the modified hot-spot model. For the single-spiral layout, the efficiency of photon detection at wavelengths smaller than λ c reaches the expected absorbance of the spiral structure and the timing jitter per unit length of the nanowire has the smallest value.